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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="rmod_4.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>;<br/>









<b>assume </b><a NAME="E1:55"/>
<font color="Maroon">L</font> is    <a href="rmod_4.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b>
(  <a href="rmod_4.html#K2" target="_self">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="rmod_4.html#K7" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">L</font> &amp;  <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:55"/><b>then </b>
 <a href="rmod_4.html#K2" target="_self">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="rmod_4.html#K7" target="_self">*</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
<font color="Maroon">L</font> <a href="rmod_4.html#K7" target="_self">*</a> <font color="Maroon">a</font> is    <a href="rmod_4.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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